English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This paper studies a small-gain theorem for nonlinear stochastic equations driven by additive white noise in both trajectories and stationary distribution. Motivated by the most recent work of Marcondes de Freitas and Sontag [SIAM J. Control Optim., 53 (2015), pp. 2657--2695], we first define the input-to-state characteristic operator $mathcal{K}(u)$ of the system in a suitably chosen input space via a backward Ito integral, and then for a given output function $h$ we define the gain operator as the composition of output function $h$ and the input-to-state characteristic operator $mathcal{K}(u)$ on the input space. Suppose that the output function is either order-preserving or anti-order-preserving in the usual vector order and the global Lipschitz constant of the output function is less than the absolute of the negative principal eigenvalue of the linear matrix. Then we prove the so-called small-gain theorem: the gain operator has a unique fixed point; the image for the input-to-state characteristic op...

A Small-Gain Theorem for Nonlinear Stochastic Systems with Inputs and Outputs I: Additive White Noise